Hyperbolic side-side-angle ambiguity
= Hyperbolic side-side-angle ambiguity
{title2=$c_\pm=\ln(3\pm\sqrt2)$}
Two corresponding side lengths and an equal nonincluded angle need not determine a <hyperbolic triangle>. Set $A=\pi/6$, $\cosh a=3/2$, $\cosh b=2$. The <hyperbolic law of cosines> has two distinct positive solutions $c=\ln(3\pm\sqrt2)$. The two triangles share $a,b,A$ but have different third sides. An included angle instead determines the third side by the cosine rule.